The invention is based on a fuel injection pump for internal combustion engines, having a pump piston provided with control grooves and distributor grooves arranged to operate within a pump head, and wherein the respective grooves communicate with an intake conduit which leaks from a suction chamber to a pump work chamber, the pump also being provided with pressure lines leading to forechambers of the injection valves, and with a relief line leading through the pump piston to the suction chamber, and further having a governor slide movably disposed on the pump piston and arranged to control a relief conduit carried within the pump piston from the pump work chamber to the suction chamber, and also having an electrical shutoff device. In known fuel injection pumps of this kind, if the rpm governor (henceforth called simply "governor") which controls the governor slide on the pump piston fails, or if the governor slide seizes on the pump piston, it is no longer possible to open the relief conduit. As a result, the maximum permissible rpm of the fuel injection pump can no longer be adhered to via the governor. The internal combustion engine must then be shut off immediately via the electrical shutoff device and accordingly via the ignition key by the vehicle driver himself, in order to avoid an undesirable overspeeding of the engine. However, the disadvantage then is that the steering wheel locking mechanism may be turned on by the actuation of the ignition key, in which case the vehicle can no longer be controlled.